Theorems · Theorem · logic and foundations
Set.empty_ne_univ
∀ {α : Type u} [Nonempty α], ∅ ≠ Set.univ- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement and proof · cited by 3,945
- Set.univ_eq_empty_iffproof · cited by 13
- not_isEmpty_of_nonemptyproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- AddSubgroup.exists_finiteIndex_of_leftCoset_coverproof · cited by 2
- AddSubgroup.exists_finiteIndex_of_leftCoset_cover_auxproof · cited by 2
- Subgroup.exists_finiteIndex_of_leftCoset_coverproof · cited by 1
- Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- AffineSubspace.bot_ne_topproof · cited by 1